In an optical fiber communication system, it is an important problem to improve a receiving sensitivity to expand a transmission distance. Recently, thanks to rapid progress of a digital coherent technology by a combination of digital signal processing (DSP) and a coherent transmission technology, selections of modulation formats in optical communications have largely been widened. Therefore, there have been made many attempts to improve the receiving sensitivity by innovation of the modulation format.
Polarization-switched quadrature phase-shift keying (PS-QPSK) may be exemplified as a representative high receiving sensitivity modulation system. The PS modulation is modulation for switching the momentary polarization between two quadrature polarizations (X and Y) in response to data of 0 or 1, and thereby, an information amount of one bit/symbol can be added as compared to a single polarization signal having the same multi-valued degrees. The PS-QPSK is modulation of a total of three bits/symbol by a combination of the QPSK of two bits/symbol and the PS modulation.
As to an optical modulation system utilizing the polarization, a polarization division multiplexing (PDM) system that uses two quadrature polarizations respectively as independent channels is widely known. The PDM can double the information amount as compared to the single polarization signal (2×2=4 bits/symbol in case of PDM-QPSK). On the other hand, the receiving sensitivity in the same symbol rate is reduced to a half as compared to that in the single polarization signal. Since the modulation is momentarily performed by the single polarization in a case of the PS modulation, the information amount can be increased without deteriorating the receiving sensitivity.
In fact, Non-Patent Literature 1 shows that a signal point arrangement of PS-QPSK is an optimal arrangement in view of receiving sensitivity in a four dimensional space having respective components of X polarization in-phase (XI), X polarization quadrature (XQ), Y polarization in-phase (YI) and Y polarization quadrature (YQ) as a base. Further, also in Non-Patent literature 2, long distance transmission of 13600 km using a PS-QPSK signal of 42.7 Gbps is reported, which experimentally indicates that the PS-QPSK can be sufficiently applied also to the long distance transmission in the degree of Pacific Ocean crossing.
As to a method of generating the PS-QPSK signal, two kinds of methods shown in FIG. 2 in Non-patent Literature 1 are well known. That is, one is a method (conventional art 1) for serially connecting a QPSK modulator and a polarization modulator, and the other is a method (conventional art 2) in which a PDM-QPSK modulator is used, and a particular correlation is formed between signals of four lines driving the PDM-QPSK modulator, whereby a half of signal points of the PS-QPSK is thinned out to generate the PS-QPSK signal.
FIG. 1 shows a configuration example of a modulator using the conventional art 1. In this example, a QPSK modulation unit 191 is serially connected to a polarization modulation unit 192. In FIG. 1, the QPSK modulation unit 191 has a general configuration, that is, the configuration in which an optical splitting circuit having an optical intensity splitting ratio of 1:1 (0.5:0.5) and an optical coupling circuit having an optical coupling ratio of 1:1 (0.5:0.5) are provided, and BPSK modulation units 111 and 112 that perform binary phase modulation (Binary-PSK: BPSK) are respectively arranged in the respective arms in a Mach-Zehnder (MZ) circuit configured of the splitting and coupling circuits, and further, a phase shifter 121 is provided in the one-side arm for making a phase change of π/2. It is the most general to use an MZ circuit having high-speed phase modulation units in both the arms (hereinafter, simply “MZ modulation circuit”) as the BPSK modulation unit. The BPSK modulation units 111 and 112 and the polarization modulation unit 192 are respectively driven by binary data signals d1, d2, and d3.
In this example, there will be considered a case where operation polarization of the BPSK modulation units 111 and 112 is set to X polarization, and X polarization continuous light of intensity 1 is input to a main input port 101. When an input optical field to the main input port 101 expressed by Jones vector of X, Y base (the 1st row corresponds to X polarization, and the 2nd row corresponds to Y polarization) is indicated at Ein, and an output optical filed from a main output port 102 is indicated at Eout, Eout can be expressed according to the following equation.
                    [                  Formula          ⁢                                          ⁢          1                ]                                                                                  E            out                    =                                    T              2                        ⁢                          T              1                        ⁢                          E              in                                      ⁢                                  ⁢                                                                              T                  1                                =                                ⁢                                  (                                                                                                                                                                                                                                          r                                  1                                                                ⁢                                                                  r                                  2                                                                                                                      ⁢                                                          b                              1                                                                                +                                                                                    ⅇ                                                              j                                ⁢                                                                  π                                  2                                                                                                                      ⁢                                                                                                                            (                                                                      1                                    -                                                                          r                                      1                                                                                                        )                                                                ⁢                                                                  (                                                                      1                                    -                                                                          r                                      2                                                                                                        )                                                                                                                      ⁢                                                          b                              2                                                                                                                                                  0                                                                                                            0                                                                    a                                                                              )                                                                                                        =                                ⁢                                                      1                    2                                    ⁢                                      (                                                                                                                                                      b                              1                                                        +                                                          j                              ⁢                                                                                                                          ⁢                                                              b                                2                                                                                                                                                              0                                                                                                                      0                                                                          a                                                                                      )                                                                                      ⁢                                  ⁢                              T            2                    =                      (                                                            p                                                  0                                                                                                  1                    -                    p                                                                    0                                                      )                          ⁢                                  ⁢                              E            in                    =                                                    (                                                                            1                                                                                                  0                                                                      )                            ⁢                                                          ∴                              E                out                                      =                                          1                2                            ⁢                              (                                                                                                    p                        ⁡                                                  (                                                                                    b                              1                                                        +                                                          j                              ⁢                                                                                                                          ⁢                                                              b                                2                                                                                                              )                                                                                                                                                                                                  (                                                      1                            -                            p                                                    )                                                ⁢                                                  (                                                                                    b                              1                                                        +                                                          j                              ⁢                                                                                                                          ⁢                                                              b                                2                                                                                                              )                                                                                                                    )                                                                        (                  Equation          ⁢                                          ⁢          1                )            
Herein, T1 and T2 respectively are Jones matrixes of X, Y base expressing transmission characteristics of the QPSK modulation unit 191 and the polarization modulation unit 192. r1 is an optical intensity splitting ratio of the optical splitting circuit 131 and r2 is an optical coupling ratio of the optical coupling circuit 132, and in the present embodiment, r1=r2=0.5. b1 and b2 are respectively modulation parameters of the BPSK modulation units 111 and 112, and have either one of +1 or −1 in a symbol point (center timing of a symbol on time axis). p is a modulation parameter of the polarization modulation unit 192, and has either one of 1 or 0 in a symbol point. a is transmittance of the QPSK modulation unit 191 to Y polarization, and since input light to the modulation unit is X polarization, a value of a does not affect the output light.
It should be noted that in the present specification, the optical splitting unit, the optical coupling unit, the BPSK modulation unit, other circuit elements (including a polarization rotating unit and a polarization coupling unit which will be described later), and optical waveguides for connecting them are all assumed to be in an ideal state where the excessive loss is zero, for model simplification. All the circuit elements except the polarization modulation unit and the polarization rotating unit are assumed to be in an ideal state where the polarization rotation is not generated (that is, in a state where off-diagonal elements of Jones matrix are zero).
FIG. 2A, FIG. 2B and FIG. 2C show two kinds of diagrams indicating a relation between d1 to d3 and Eout in the modulator configuration shown in FIG. 1. FIG. 2A and FIG. 2B are respectively complex signal diagrams each having an X polarization component and a Y polarization component. The respective lateral axes indicate optical electrical field amplitudes EXI and EYI of I phase, and the respective vertical axes indicate optical electrical field amplitudes EXQ and EYQ of Q phase. Next, for distinction from FIG. 2C to be described, such a diagram is hereinafter called “IQ diagram”. FIG. 2C is a diagram where a lateral axis indicates phase φX′ of an X′ polarization component and a vertical axis indicates phase φY′ of a Y′ polarization component. As shown in FIG. 10, however, X′ polarization axis and X polarization axis, and Y′ polarization axis and Y polarization axis are respectively defined to be shifted by 45 degrees with each other. In addition, an indication range (entire width) of each of the lateral axis and the vertical axis is set to 2π. This diagram is often used for expressing PS-QPSK signal point arrangement (for example, Non-Patent Literature 3), and this diagram is hereinafter called “XY diagram” for distinction from FIG. 2A and FIG. 2B.
A relation between Jones vector Eout of the output optical light, and vertical axis values and lateral axis values of the respective diagrams (EXI, EXQ, EYI, EYQ, φX′ and φY′) will be put in order as follows.
                    [                  Formula          ⁢                                          ⁢          2                ]                                                                                                                                  E                  out                                =                                ⁢                                  (                                                                                                                                          E                            XI                                                    +                                                      j                            ⁢                                                                                                                  ⁢                                                          E                              XQ                                                                                                                                                                                                                                                E                            YI                                                    +                                                      j                            ⁢                                                                                                                  ⁢                                                          E                              YQ                                                                                                                                                            )                                                                                                        =                                ⁢                                                      1                                          2                                                        ⁢                                      (                                                                                            1                                                                          1                                                                                                                                                  -                            1                                                                                                    1                                                                                      )                                    ⁢                                      (                                                                                                                                                      A                              X                              ′                                                        ⁢                                                          exp                              ⁡                                                              (                                                                  j                                  ⁢                                                                                                                                          ⁢                                                                      ∅                                                                          X                                      ′                                                                                                                                      )                                                                                                                                                                                                                                                                    A                              Y                              ′                                                        ⁢                                                          exp                              ⁡                                                              (                                                                  j                                  ⁢                                                                                                                                          ⁢                                                                      ∅                                                                          Y                                      ′                                                                                                                                      )                                                                                                                                                                          )                                                                                      ⁢                                  ⁢                              A            X            ′                    =                                    1                              2                                      ⁢                                                                                (                                                                  E                        XI                                            -                                              E                        YI                                                              )                                    2                                +                                                      (                                                                  E                        XQ                                            -                                              E                        YQ                                                              )                                    2                                                                    ⁢                                  ⁢                              A            Y            ′                    =                                    1                              2                                      ⁢                                                                                (                                                                  E                        XI                                            +                                              E                        YI                                                              )                                    2                                +                                                      (                                                                  E                        XQ                                            +                                              E                        YQ                                                              )                                    2                                                                    ⁢                                  ⁢                              ϕ            X            ′                    =                      arg            ⁢                          {                                                E                  XI                                -                                  E                  YI                                +                                  j                  ⁡                                      (                                                                  E                        XQ                                            -                                              E                        YQ                                                              )                                                              }                                      ⁢                                  ⁢                              ϕ            Y            ′                    =                      arg            ⁢                          {                                                E                  XI                                +                                  E                  YI                                +                                  j                  ⁡                                      (                                                                  E                        XQ                                            +                                              E                        YQ                                                              )                                                              }                                                          (                  Equation          ⁢                                          ⁢          2                )            
It should be noted that in the modulation system which does not include intensity modulation, such as PS-QPSK, PDM-QPSK or the like, AX′ and AY′ always have constant values. Therefore, φX′ and φY′ are sufficient as parameters for expressing the signal point arrangement, and the arrangement of all the signal points can be expressed by a single diagram when the XY diagram is used.
According to Equation 1 and Equation 2, a relation between vertical axis values and lateral axis values of the respective diagrams and modulation parameters of the respective modulation units is as follows.
                    [                  Formula          ⁢                                          ⁢          3                ]                                                                                  E            XI                    =                                    1              2                        ⁢                          pb              1                                      ⁢                                  ⁢                              E            XQ                    =                                    1              2                        ⁢                          pb              2                                      ⁢                                  ⁢                              E            YI                    =                                    1              2                        ⁢                          (                              1                -                p                            )                        ⁢                          b              1                                      ⁢                                  ⁢                              E            YQ                    =                                    1              2                        ⁢                          (                              1                -                p                            )                        ⁢                          b              2                                      ⁢                                  ⁢                              ϕ            X            ′                    =                      arg            ⁢                          {                                                                    (                                                                  2                        ⁢                                                                                                  ⁢                        P                                            -                      1                                        )                                    ⁢                                      b                    1                                                  +                                                      j                    ⁡                                          (                                                                        2                          ⁢                                                                                                          ⁢                          p                                                -                        1                                            )                                                        ⁢                                      b                    2                                                              }                                      ⁢                                  ⁢                              ϕ            Y            ′                    =                      arg            ⁢                          {                                                b                  1                                +                                  j                  ⁢                                                                          ⁢                                      b                    2                                                              }                                                          (                  Equation          ⁢                                          ⁢          3                )            
[d1d2d3] in FIG. 2A, FIG. 2B, and FIG. 2C indicate mapping of drive binary data to the respective signal points. A data bit value is associated with a value of a modulation parameter in each BPSK modulation unit in a symbol point in a one-to-one relation. Herein, as to the BPSK modulators 111 and 112 (n=1, 2) in FIG. 1, when dn=0, bn=+1 (phase 0), and when dn=1, bn=−1 (phase π). In addition, as to the polarization modulation unit 192 in FIG. 1, when d3=0, p=1, and when d3=1, p=0. According to the above corresponding relation and the Equation 3, the mapping shown in each of FIG. 2A, FIG. 2B and FIG. 2C can be obtained.
As shown in the IQ amplitude diagram in each of FIG. 2A and FIG. 2B, when d3=0, signal intensity of Y polarization is zero, when d3=1, signal intensity of X polarization is zero, and a signal state in a polarization side of intensity non-zero takes four values equivalent to the QPSK signal arrangement corresponding to d1 and d2.
As shown in FIG. 2C, when the XY diagram is used, signal points of 23=8 points of PS-QPSK which is three bits/symbol modulation can be all expressed at a time. When an output signal is X polarization (d3=0), a phase difference between X′ component and Y′ component is zero. Therefore, the corresponding point is on a straight line of inclination 1 passing through the origin. When the output signal is Y polarization (d3=1), the phase difference between X′ component and Y′ component is π. Therefore, the corresponding point is on a straight line where the section is π or −π, and the inclination is 1.
FIG. 3 shows a modulator configuration example using the conventional art 2. In this example, a PDM-QPSK modulator 300 is used. The PS-QPSK 300 uses a general configuration, that is, the configuration that QPSK modulation units 391 and 392 having the same configuration as that of the conventional art 1 are connected to the respective outputs of an optical splitting unit 330 having a splitting ratio of 1:1, the output of the QPSK modulation unit 391 is connected directly to a polarization coupling unit 352, and the output of the QPSK modulation unit 392 is connected through a 90-degree polarization rotating unit 351 to the polarization coupling unit 352. BPSK modulation units 311 to 314 are respectively driven by binary data signals d1 to d4. Among them, d1 to d3 use independent data signals, and d4 is generated to be [Formula 4: d4=(d1 ⊕d2)⊕d3] ([Formula 5: “⊕”] expresses XOR calculation).
Hereinafter, there will be considered a case where operation polarization of the BPSK modulation units 311 and 314 is indicated at X′ for descriptive purposes, and X′ polarization continuous light of intensity 1 is input to a main input port 301. When Jones vector of X′, Y′ base (the 1st row corresponds to X′ polarization and the 2nd row corresponds to Y′ polarization) of output light from a main output port 302 is indicated at Eout, and Jones vector of X, Y base (the 1st row corresponds to X polarization and the 2nd row corresponds to Y polarization) is indicated at Eout, the following relation is established.
                    [                  Formula          ⁢                                          ⁢          6                ]                                                                                  E            out            ′                    =                                    {                                                                    S                    1                    ′                                    ⁢                                      T                    1                    ′                                    ⁢                                      1                                          2                                                                      +                                                      S                    2                    ′                                    ⁢                                      R                    ′                                    ⁢                                      T                    2                    ′                                    ⁢                                      1                                          2                                                                                  }                        ⁢                          (                                                                    1                                                                                        0                                                              )                                      ⁢                                  ⁢                              T            1            ′                    =                                    1              2                        ⁢                          (                                                                                                                  b                        1                                            +                                              j                        ⁢                                                                                                  ⁢                                                  b                          2                                                                                                                          0                                                                                        0                                                                              a                      1                                                                                  )                                      ⁢                                  ⁢                              T            2            ′                    =                                    1              2                        ⁢                          (                                                                                                                  b                        3                                            +                                              j                        ⁢                                                                                                  ⁢                                                  b                          4                                                                                                                          0                                                                                        0                                                                              a                      2                                                                                  )                                      ⁢                                  ⁢                              R            ′                    =                      (                                                            0                                                                      -                    1                                                                                                1                                                  0                                                      )                          ⁢                                  ⁢                              S            1            ′                    =                      (                                                            1                                                  0                                                                              0                                                  0                                                      )                          ⁢                                  ⁢                              S            2            ′                    =                                                    (                                                                            0                                                              0                                                                                                  0                                                              1                                                                      )                            ⁢                                                          ∴                              E                out                ′                                      =                                          1                                  2                  ⁢                                      2                                                              ⁢                              (                                                                                                                              b                          1                                                +                                                  j                          ⁢                                                                                                          ⁢                                                      b                            2                                                                                                                                                                                                                            b                          3                                                +                                                  j                          ⁢                                                                                                          ⁢                                                      b                            4                                                                                                                                              )                                                    ⁢                                  ⁢                                                                              E                  out                                =                                ⁢                                                      1                                          2                                                        ⁢                                      (                                                                                            1                                                                          1                                                                                                                                                  -                            1                                                                                                    1                                                                                      )                                    ⁢                                      Eout                    ′                                                                                                                          =                                ⁢                                                      1                    4                                    ⁢                                      (                                                                                                                                                      b                              1                                                        +                                                          b                              3                                                        +                                                          j                              ⁡                                                              (                                                                                                      b                                    2                                                                    +                                                                      b                                    4                                                                                                  )                                                                                                                                                                                                                                                                    -                                                              b                                1                                                                                      +                                                          b                              3                                                        +                                                          j                              ⁡                                                              (                                                                                                      -                                                                          b                                      2                                                                                                        +                                                                      b                                    4                                                                                                  )                                                                                                                                                                          )                                                                                                          (                  Equation          ⁢                                          ⁢          4                )            
Here, T1′ and T2′ are respectively Jones matrixes of X′, Y′ base expressing transmission characteristics of the QPSK modulation units 391 and 392, R′ is Jones matrix of X′, Y′ base expressing transmission characteristics of the 90-degree polarization rotating unit 351, S1′ and S2′ are respectively Jones matrixes of X′, Y′ base expressing transmission characteristics of the polarization coupling unit 352 to inputs from a port 1 (side of the QPSK modulation units 391) and a port 2 (side of the QPSK modulation unit 392). A coefficient
  [      Formula    ⁢                  ⁢    7    ⁢          :        ⁢                  ⁢          1              2              ]of a right side in the first line expresses a branch by the optical splitting unit 330. b1 to b4 are respectively modulation parameters of the BPSK modulation units 311 to 314, and take either one of +1 or −1 in a symbol point (center timing of a symbol on time axis). a1 and a2 are respectively transmittances of the QPSK modulation units 391 and 392 to Y′ polarization, and since input light to the modulation unit is X′ polarization, values of a1 and a2 do not affect the output light.
According to Equation 2 and Equation 4, the following relation is established in the present example.
                    [                  Formula          ⁢                                          ⁢          8                ]                                                                                  E            XI                    =                                    1              4                        ⁢                          (                                                b                  1                                +                                  b                  3                                            )                                      ⁢                                  ⁢                              E            XQ                    =                                    1              4                        ⁢                          (                                                b                  2                                +                                  b                  4                                            )                                      ⁢                                  ⁢                              E            YI                    =                                    1              4                        ⁢                          (                                                -                                      b                    1                                                  +                                  b                  3                                            )                                      ⁢                                  ⁢                              E            YQ                    =                                    1              4                        ⁢                          (                                                -                                      b                    2                                                  +                                  b                  4                                            )                                      ⁢                                  ⁢                              ϕ            X            ′                    =                      arg            ⁢                          {                                                b                  1                                +                                  j                  ⁢                                                                          ⁢                                      b                    2                                                              }                                      ⁢                                  ⁢                              ϕ            Y            ′                    =                      arg            ⁢                          {                                                b                  3                                +                                  j                  ⁢                                                                          ⁢                                      b                    4                                                              }                                                          (                  Equation          ⁢                                          ⁢          5                )            
FIG. 4B shows an XY diagram expressing a relation between d1 to d4 and Eout in the modulator configuration shown in FIG. 3. [d1 d2 d3 d4] in the figure indicates mapping of drive binary data to each signal point. A data bit value is associated with a value of a modulation parameter in each BPSK modulation unit in a symbol point in a one-to-one relation. Herein, when dn=0, bn=+1 (phase 0), and when dn=1, bn=−1 (phase π). According to the above corresponding relation and Equation 5, the mapping shown in FIG. 4B can be obtained.
For facilitating understanding of the operation principle in the present example, FIG. 4A firstly shows a signal point arrangement in a case where all of d1 to d4 are provided as independent data, that is, in a case of a regular PDM-QPSK drive. It is found out that signal points of 24=16 points of PDM-QPSK which is four bits/symbol modulation are arranged in a lattice shape of 4×4. [d1 d2] corresponds to a lateral axis and [d3 d4] corresponds to a vertical axis.
Next, by referring to FIG. 4B, it is found out that by associating d4 with d1 to d3 as [Formula 9: d4=(d1⊕d2)⊕+d3] according to the drive method in this example, a half of the signal points are thinned out to produce a signal point arrangement of PS-QPSK as similar to that of FIG. 2C.